Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
331 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#4683 | C2 | semidirect |
| 3. C32×#346 | C2 | semidirect |
| 4. C3×#4509 | C2 | semidirect |
| 6. #69080 | C3 | direct (N × H) |
| 18. #4683 | C2×C3 | semidirect |
| 21. C3×#346 | D3 | semidirect |
| 22. C3×#346 | C2×C3 | semidirect |
| 23. #4509 | C2×C3 | semidirect |
| 65. #346 | C3×D3 | semidirect |
| 158. C32 | #2244 | semidirect |
| 184. C3 | #69080 | direct (N × H) |
| 185. C3 | C3×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4695 | 2 |
| C3×#4683 | 2 |
| C32×#346 | 2 |
| C3×#4509 | 2 |
| C3×#2244 | 3 |
| #69080 | 3 |